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On the Formalization of Some Results of Context-Free Language Theory

  • Marcus Vinícius Midena Ramos
  • Ruy J. G. B. de Queiroz
  • Nelma Moreira
  • José Carlos Bacelar Almeida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9803)

Abstract

This work describes a formalization effort, using the Coq proof assistant, of fundamental results related to the classical theory of context-free grammars and languages. These include closure properties (union, concatenation and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. This is probably the most comprehensive formalization of the classical context-free language theory in the Coq proof assistant done to the present date, and includes the important result that is the formalization of the Pumping Lemma for context-free languages.

Keywords

Context-free language theory Language closure Grammar simplification Chomsky Normal Form Pumping Lemma Formalization Coq 

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Marcus Vinícius Midena Ramos
    • 1
    • 2
  • Ruy J. G. B. de Queiroz
    • 2
  • Nelma Moreira
    • 3
  • José Carlos Bacelar Almeida
    • 4
    • 5
  1. 1.Universidade Federal do Vale do São FranciscoJuazeiroBrazil
  2. 2.Universidade Federal de PernambucoRecifeBrazil
  3. 3.Universidade do PortoPortoPortugal
  4. 4.Universidade do MinhoBragaPortugal
  5. 5.HASLab-INESC TECPortoPortugal

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